Optimal control of convection-cooling and numerical implementation

This paper is concerned with the problem of enhancing convection-cooling via active control incompressible velocity field, described by a stationary diffusion–convection model. essentially leads to bilinear optimal problem. A rigorous proof existence an presented and first order optimality conditions are derived for solving using variational inequality. Moreover, second sufficient established characterize local minimizer. Finally, numerical experiments conducted utilizing finite elements methods together nonlinear iterative schemes, demonstrate validate effectiveness our design.